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arXiv · 2009.06464

On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two

Srilakshmi Krishnamoorthy·Sunil Kumar Pasupulati
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Abstract

Lenstra introduced the notion of a Euclidean ideal class, which is a generalization of the Euclidean domain. Lenstra also proved that the Euclidean ideal in a number field $K$ implies that the class group of $K$ is cyclic. We construct a family of biquadratic fields with a Euclidean ideal whenever the class number is 2. This extends the families given by Graves, Hsu, Chattopadhyay, and Muthukrishnan.

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Srilakshmi Krishnamoorthy, Sunil Kumar Pasupulati. 2020-09-14. On the existence of a non-principal Euclidean ideal class in biquadratic fields with class number two. https://arxiv.org/abs/2009.06464

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